Finally, results from Gravity Probe-B

Nearly fifty years after its inception, the Gravity Probe B satellite mission delivers the first measurements of how a spinning gyroscope precesses in the gravitational warping of spacetime.Comment: A Viewpoint article, published in Physics 4, 43 (2011), available at http://physics.aps.org/articles/v4/43 Submitted to the arXiv by permission of the American Physical Societ

Post-Newtonian constraints on f(R) cosmologies in metric formalism

We compute the complete post-Newtonian limit of the metric form of f(R) gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian f(R) must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that the lagrangian f(R) must be almost linear in R and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot be responsible for the observed cosmic speed-up.Comment: 10 pages, no figures, revtex

Capture of non-relativistic particles in eccentric orbits by a Kerr black hole

We obtain approximate analytic expressions for the critical value of the total angular momentum of a non-relativistic test particle moving in the Kerr geometry, such that it will be captured by the black hole. The expressions apply to arbitrary orbital inclinations, and are accurate over the entire range of angular momentum for the Kerr black hole. The expressions can be easily implemented in N-body simulations of the evolution of star clusters around massive galactic black holes, where such captures play an important role.Comment: 8 pages, 1 figure, published versio

Constraining Lorentz-violating, Modified Dispersion Relations with Gravitational Waves

Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton's momentum and deteriorate for a steeper scaling.Comment: 11 pages, 3 figures, 2 tables: title changed slightly, published versio

Bisimple monogenic orthodox semigroups

We give a complete description of the structure of all bisimple orthodox semigroups generated by two mutually inverse elements

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. IV. Radiation reaction for binary systems with spin-spin coupling

Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies, including spin-spin effects. In particular we determine the effects of radiation-reaction coupled to spin-spin effects on the two-body equations of motion, and on the evolution of the spins. We find that radiation damping causes a 3.5PN order, spin-spin induced precession of the individual spins. This contrasts with the case of spin-orbit coupling, where there is no effect on the spins at 3.5PN order. Employing the equations of motion and of spin precession, we verify that the loss of total energy and total angular momentum induced by spin-spin effects precisely balances the radiative flux of those quantities calculated by Kidder et al.Comment: 10 pages, coincides with published versio

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. V. Evidence for the strong equivalence principle to second post-Newtonian order

Using post-Newtonian equations of motion for fluid bodies valid to the second post-Newtonian order, we derive the equations of motion for binary systems with finite-sized, non-spinning but arbitrarily shaped bodies. In particular we study the contributions of the internal structure of the bodies (such as self-gravity) that would diverge if the size of the bodies were to shrink to zero. Using a set of virial relations accurate to the first post-Newtonian order that reflect the stationarity of each body, and redefining the masses to include 1PN and 2PN self-gravity terms, we demonstrate the complete cancellation of a class of potentially divergent, structure-dependent terms that scale as s^{-1} and s^{-5/2}, where s is the characteristic size of the bodies. This is further evidence of the Strong Equivalence Principle, and supports the use of post-Newtonian approximations to derive equations of motion for strong-field bodies such as neutron stars and black holes. This extends earlier work done by Kopeikin.Comment: 14 pages, submitted to Phys. Rev. D; small changes to coincide with published versio

The ORNL-SNAP shielding program

The effort in the ORNL-SNAP shielding program is directed toward the development and verification of computer codes using numerical solutions to the transport equation for the design of optimized radiation shields for SNAP power systems. A brief discussion is given for the major areas of the SNAP shielding program, which are cross-section development, transport code development, and integral experiments. Detailed results are presented for the integral experiments utilizing the TSF-SNAP reactor. Calculated results are compared with experiments for neutron and gamma-ray spectra from the bare reactor and as transmitted through slab shields

Carter-like constants of the motion in Newtonian gravity and electrodynamics

For a test body orbiting an axisymmetric body in Newtonian gravitational theory with multipole moments Q_L, (and for a charge in a non-relativistic orbit about a charge distribution with the same multipole moments) we show that there exists, in addition to the energy and angular momentum component along the symmetry axis, a conserved quantity analogous to the Carter constant of Kerr spacetimes in general relativity, if the odd-L moments vanish, and the even-L moments satisfy Q_2L = m (Q_2/m)^L. Strangely, this is precisely the relation among mass moments enforced by the no-hair theorems of rotating black holes. By contrast, if Newtonian gravity is supplemented by a multipolar gravitomagnetic field, whose leading term represents frame-dragging (or if the electrostatic field is supplemented by a multipolar magnetic field), we are unable to find an analogous Carter-like constant. This further highlights the very special nature of the Kerr geometry of general relativity.Comment: 4 page

Propagation Speed of Gravity and the Relativistic Time Delay

We calculate the delay in the propagation of a light signal past a massive body that moves with speed v, under the assumption that the speed of propagation of the gravitational interaction c_g differs from that of light. Using the post-Newtonian approximation, we consider an expansion in powers of v/c beyond the leading ``Shapiro'' time delay effect, while working to first order only in Gm/c^2, and show that the altered propagation speed of the gravitational signal has no effect whatsoever on the time delay to first order in v/c beyond the leading term, although it will have an effect to second and higher order. We show that the only other possible effects of an altered speed c_g at this order arise from a modification of the parametrized post-Newtonian (PPN) coefficient \alpha_1 of the metric from the value zero predicted by general relativity. Current solar-system measurements already provide tight bounds on such a modification. We conclude that recent measurements of the propagation of radio signals past Jupiter are sensitive to \alpha_1, but are not directly sensitive to the speed of propagation of gravity.Comment: Revised, 15 pages, 1 figure, accepted for publication in The Astrophysical Journa